An Attempt to Understand Reality

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Recently I began compiling something of a list of, what appear to be, commonly appealed to “trump cards” by certain Christians during attempts at rational dialogue. While I certainly don’t intend to implicate all Christians (or even only Christians), I have noticed a regular occurrence of these “moves” in a multitude of discussions. In Part 1 I briefly discussed the appeal to faith. From my own experience discussions seem to either begin or end with this “trump card”. For part 2 I would like to analyze what seems to be a background assumption of many Christians. This “trump card” isn’t necessarily appealed to directly; it most often operates behind the scenes, but has noticeable effects. Here it is:

A: If one does not believe that Christianity is true, then that person hates God and rejects “His” gift of salvation.

The difficulty with this background assumption is that it goes to the heart of the Christian message. Humans are the creation of God, but are separated from “Him” because of sin. Ultimately, this means that humans are headed for one of two fates: eternal heaven or eternal hell. Those who repent and accept Christ are granted eternal heaven, while those who do not get eternal hell.

Now, eternal hell (which is generally taken as never-ending punishment) is rather harsh. So, to alleviate the uncomfortable dissonance, it is my opinion that many Christians are driven to hold A. It is much easier to believe that unrepentant God-haters who despise “His” sacrifice deserve never-ending punishment than it is to accept that honest seekers and skeptics could somehow “miss the boat” and end up in eternal torment.

The problem, of course, is that A is a completely unwarranted assumption. More than that, it is unfalsifiable in the sense that all counter-examples can be dismissed. Since no one can expose his or her first person perspective to direct analysis, we must always go off of what people report about themselves. The person who accepts A, however, can simply maintain that the non-believer is deceiving himself or herself by suppressing the truth (more on that at a later time).

Nevertheless, let’s take a look at A itself and see if it makes better sense to adopt its negation. Note that A is a conditional statement. Let C stand for the simple proposition A person P believes that Christianity is true. Let H represent the proposition P hates God and rejects “His” gift of salvation. Then the assumption A can be expressed as

The negation of this is therefore

In English this would read

: Person P does not believe that Christianity is true, but does not hate God or reject “His” gift of salvation.

Let’s see why is more likely true than . If we look again at the component propositions and we run into an immediate problem. Notice that is a proposition that refers to the noetic status of a person. It makes a claim about what a person believes. In other words, it reports that some person takes the Christian system of belief to be false or not to correspond to reality. The proposition , by contrast, refers to a directed feeling or emotion of a person. So, the assumption claims that a certain state of unbelief with respect to some propositions implies an associated emotion with respect to the content of those propositions. This is a very queer claim indeed. Generally, the status of one’s belief has no connection to how one feels about the content of the belief. For instance, I don’t believe in fire-breathing dragons. In other words, I take it that they do not exist. But this says nothing of how I feel about fire-breathing dragons. In fact, I think fire-breathing dragons, while scary, are pretty awesome. So, if this connection fails to hold in general, why should we believe it holds in the specific case of Christianity? It is true that some people hate the idea of the Christian God, but there is no evidence to suggest that every non-believer does.

The underlying issue here is that many Christians conflate two types of “rejection”. Let’s call the first type of rejection relational rejection and the second type propositional rejection. Relational rejection involves rejecting a person or something a person is offering. It involves a negative feeling toward the person or thing offered by the person. For instance, if a boy asks out a girl and she says “no”, then she has relationally rejected the poor boy. She is saying that she does not like the idea of having a particular type of relationship with him. Propositional rejection, by contrast, is simply to not accept a proposition as being true. For example, suppose a girl is asked whether she thinks that some boy will ask her out. Suppose she says “no”. Then in this case she is engaging in propositional rejection. That is, she is rejecting the proposition that some boy is going to ask her out. Notice that this rejection says absolutely nothing about whether she wants the boy to ask her or not.

The confusion arises from a failure to see the distinction between the proposition that one thinks is either true or false, and the content of the proposition that one may or may not have a feeling about. For the Christian, the content of the belief is so central and personal that disbelief is automatically taken to be personal. But there is no reason to think that disbelief is always (or even often) of a personal nature. Thus, the Christian who holds is going to have to summon some really compelling evidence. Next time I’ll address one such argument claiming that truth is a person and hence rejection of the “truth” amounts to rejecting the person.

Talking with Christians (and religious people in general) is a mixed bag. Sometimes you get awesome intelligent people along with a really great discussion (even if you end up disagreeing). Most of the time, however, the discussion ends up in frustration. Having quite a bit of experience, I have put together a list of some of the most commonly used discussion killing “trump cards” played by many Christians. I’d like to address each one in a separate post. In analyzing each, I hope this will be useful to both skeptics and believers to promote more fruitful dialogue. But before I get to the list, I’d like to give an explanation as to the root of these “trump cards”.

Controlling Assumptions

While there is no doubt that humans are rational beings, there is also no doubt that humans are emotional beings. Unfortunately, at the conscious level, we are much more influenced by the latter than the former. Emotions and other psychological effects are so powerful, that humans have to work quite hard to be rational in the midst of them. This is not completely bad, since our drive, hope, and motivation are essential aspects our success. The problem is striking a correct balance, which is obviously fairly difficult.

Here lies one of the difficulties with Christianity. Not only is Christianity a system of belief, it is a system of belief saturated in emotion. It is a system designed to address the core of human longings: purpose, meaning, forgiveness, justice, belonging, love, hope, peace, etc. It provides a complete mental framework from which to operate. This, of course, is not a bad thing, but the practical effects of adopting it can make it rather difficult to maintain objectivity. One is easily blinded to the cold matters of truth when it just feels right.

This is an example of something I call a controlling assumption.

Definition [Controlling Assumption]: A controlling assumption is an assumption that once adopted sets a mental framework that interprets all data to be consistent with the assumption, even data contrary to the assumption itself.

One might describe a controlling assumption as a self-preserving assumption. It is intimately related to the idea of confirmation bias. For example, consider the famous psychological experiment where several researchers checked themselves into a mental hospital. Once admitted, they acted completely normal. One would hope that the doctors of the hospital would be able to recognize that these “impostors” were completely sane and free of mental illness. In other words, the healthy should be distinguishable from the sick. The problem, however, is that the doctors were under the influence of a controlling assumption, namely People who enter the hospital as patients have a mental illness. Because of this, the doctors interpreted the researcher’s normal behavior as symptomatic of their supposed “neuroses/psychoses”. Even as the researchers documented these things with meticulous notes, the doctors recorded in their charts that “Patients engage in note taking behavior” as if it was pathological. Ironically, those who were actually mentally ill caught on to the researchers almost immediately.

Although not always the case, the Christian belief structure can operate much like a controlling assumption, and part of the self-preserving nature of the belief structure manifests itself in various “trump cards” when being challenged. I address the first of these below.

“Trump Card” 1 -[You just have to have faith]

Generally, the very first response to any rational challenge is an appeal to faith. How “faith” is being used, however, is not generally very clear. When pressed for a definition, most respond by quoting Hebrew 11:1, which says, “Now faith is the assurance of things hoped for, the conviction of things not seen.” (NAS) Using this as a definition, what the Christian is saying is that one just needs to have assurance. My initial thought is, “Oh, is that all I need?”. Of course, even if Christianity is something I hope for, the problem is that I don’t have assurance. This is what I am seeking, but not finding. It strikes me a bit like saying to an addict who is asking how to stop, “Well, you just need to stop.” That won’t be received well, because that is the very problem that needs addressing.

The go to response from here is generally to deny that faith has anything to do with the intellect, but is a matter of the heart. Again, it isn’t at all clear what this is supposed to mean, nor is it clear where such an idea is expressed in the Bible. In fact, the Greek word for “heart” in the New Testament is καρδια or kardia, which was taken to include the whole self, including the faculty and seat of the intelligence. Thus, to say that faith is a matter of the heart and not the mind is an artificial and incorrect distinction even measured against the Bible.

Finally, telling someone that faith is required only pushes the problem back a step. Why is faith required? How does one know this? And what guides where I place my faith? After all, many religions appeal to the very same requirement. So, which does one choose? I think the issue clearly reveals that faith is not an epistemological tool that yields knowledge. This can be more rigorously demonstrated as follows.

(1) Suppose that faith provides a means of knowing something.

(2) The Christian has faith and so knows Christianity to be true.

(3) Therefore, from the definition of “know” it follows that Christianity is true.

(4) The Mormon has the same sort of faith and so knows Mormonism to be true.

(5) Therefore, Mormonism is true.

(6) Christianity and Mormonism are incompatible systems of belief.

(7) Therefore, either Christianity or Mormonism (or both) is false.

(8) If Christianity is false, then we get a contradiction with (3).

(9) Thus, Christianity must be true and Mormonism false.

(10) If Mormonism is false, then we get a contradiction with (5).

(11) Thus, Mormonism is also true, which contradicts (7).

(12) Therefore, since our initial assumption leads to a contradiction, it must be the case that (1) is false.

Of course, one could deny that Christians and Mormons have the same faith, but then one would have to wonder how we could possibly distinguish between “real” faith and “fake” faith. One would then have to appeal to something other than faith anyway.

Along with my (slow) endeavor of exploring and critiquing the ideas undergirding intelligent design, I want to resume a project I started a while back that involved addressing the claims of Chuck Missler. As I have previously mentioned, Chuck Missler is a well educated man. That being said, I also get the strong impression that Missler pretends to know a lot more than he really does. What annoys me the most is that he seems to present himself as an expert in, well, just about everything.

In his Bible studies, Missler lectures his flock on everything from cosmology to quantum mechanics to information theory and beyond. Missler has everything figured out it seems, and, while he might deny it, presents himself as having just about everything figured out. It’s shocking that he hasn’t been awarded a Nobel prize. Listening to his talks, one cannot help but be impressed by the depth and breadth of his knowledge. However, once one gets over the dazzle of Missler’s apparent expertise in everything, one begins to pick up on very questionable claims and ideas. Most of the time Missler alludes to very deep ideas, but glosses over them to spare his audience the details. OR, maybe Missler really doesn’t know or understand the details. This is my suspicion, which is motivated by several cracks in his intellectual veneer amounting to questionable claims on his part.

The first issue I’d like to address regards the size of the universe.

Missler is fond of proclaiming there are two central mathematical concepts that we don’t find in nature: Infinity and randomness. I’ll save randomness for another post.

Does Infinity Exist?

Certainly infinity exists conceptually, but the question is whether it describes anything real. In particular, Missler focuses on size. This can go in two directions: (1) small scale infinity, and (2) large scale infinity.

Small Scale ∞

Most people are familiar with number lines.

For our purposes we can focus on the interval . We can cut this interval in half and get . This can be cut in half again to get . In fact, we could carry out this cutting procedure indefinitely, always obtaining a new interval . This means that we can make the interval as small as we like. Put differently, we can cut the interval infinitely many times in the sense that there will never be a limit to the number of times we can cut the interval in half.

Now suppose that our interval models a length in space-time, say an inch. If the correspondence were true, then it would follow that space could be indefinitely halved. According to Missler, this is actually not true. It turns out that there is a limit to smallness in space-time. In other words, there is a smallest distance. This distance is known as the Planck length, which is defined by

where is Planck’s constant, is the gravitational constant, and is the speed of light. This length is exceedingly small, a mere meters (approximately). Missler is fond of saying that if at any point you divide a distance into lengths smaller than , then you lose locality, the thing you are cutting is suddenly everywhere all at once. What he concludes is that our reality is actually a “digital simulation”, terminology he uses purposely to insinuate that our world is created by God. Such loaded language seems to be characteristic of Missler.

So, what is the nature of this mysterious length? Where does it come from and how do we know it is the smallest length?

The Planck length has profound relevance in quantum gravity. Put differently, it is at this absurdly tiny scale that quantum effects become relevant and the question regards how gravity behaves or should be understood at this scale. Both general relativity and quantum field theory must be taken into account. The definition of the Planck length now makes sense since the speed of light is the natural unit that relates time and space, is the constant of gravity, and is the constant of quantum mechanics. So the Planck scale defines the meeting point of gravity, quantum mechanics, time and space.

Theoretically, it is considered problematic to think of time and space as continuous because we don’t appear to be able to meaningfully discuss distances smaller than the Planck length. Unfortunately, there is no proven physical significance to the Planck length because current technology is incapable of probing this scale. Nevertheless, current attempts to unify gravity and QM, such as String Theory and Loop Quantum Gravity, yield a minimal length, which is on the order of the Planck distance. This arises when quantum fluctuations of the gravitational field are taken into account. In the theory, distances smaller than are physically meaningless. Two “points” at distances smaller than cannot be differentiated. This seems to suggest that space-time may have a discrete or “foamy” nature rather than a continuous one. Unfortunately for Missler, however, we just don’t know at this point. Thus, the declarative nature of his claims are hasty.

Nevertheless, even if this turns out to be the case, the question becomes: what follows from that? As mentioned above, Missler is fond of saying that the universe is a “digital simulation”. Certainly the term “digital” would be apropos, but his use of “simulation” seems loaded and dubious. “Simulation” suggests that this world isn’t the “real” world. It suggests that our world merely imitates some meta-world. Of course, Missler purposely uses the term as a way to smuggle in a simulator. That simulator is God, and the meta-world is the spiritual world.

Large Scale ∞

The more questionable of Missler’s claims regards the size of the universe. He brazenly declares that we have discovered the universe to be finite. This is just flat out false, and such carelessness makes me question his credibility. It is likely that he is simply confusing the observable universe with the universe proper. There is no doubt that the observable universe is finite. It is estimated to have a radius of 46 billion light years and due to expansion grows ever larger. However, this does not necessarily imply that the universe proper is finite in size. Sir Roger Penrose, one of the most respected mathematical physicists in the world, says, “it may well be that the universe is spatially infinite, like the FLRW models with or .” (see The Road To Reality, p. 731)

Even a quick search on Wikipedia reveals that, “The size of the Universe is unknown; it may be infinite. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.”

In fact, the possibility of an infinite universe is the stuff of some multiverse models. Max Tegmark, a mathematical physicist at MIT puts it this way:

If space is infinite and the distribution of matter is sufficiently uniform on large scales, then even the most unlikely events must take place somewhere. In particular, there are infinitely many other inhabited planets, including not just one but infinitely many with people with the same appearance, name and memories as you. Indeed, there are infinitely many other regions the size of our observable universe, where every possible cosmic history is played out. This is the Level I multiverse.

Tegmark goes on

Although the implications may seem crazy and counter-intuitive, this spatially infinite cosmological model is in fact the simplest and most popular one on the market today. It is part of the cosmological concordance model, which agrees with all current observational evidence and is used as the basis for most calculations and simulations presented at cosmology conferences. In contrast, alternatives such as a fractal universe, a closed universe and a multiply connected universe have been seriously challenged by observations. Yet the Level I multiverse idea has been controversial (indeed, an assertion along these lines was one of the heresies for which the Vatican had Giordano Bruno burned at the stake in 1600†), so let us review the status of the two assumptions (infinite space and “sufficiently uniform” distribution). How large is space? Observationally, the lower bound has grown dramatically (Figure 2) with no indication of an upper bound. We all accept the existence of things that we cannot see but could see if we moved or waited, like ships beyond the horizon. Objects beyond cosmic horizon have similar status, since the observable universe grows by a light-year every year as light from further away has time to reach us‡. Since we are all taught about simple Euclidean space in school, it can therefore be difficult to imagine how space could not be infinite — for what would lie beyond the sign saying“SPACE ENDS HERE — MIND THE GAP”? Yet Einstein’s theory of gravity allows space to be finite by being differently connected than Euclidean space, say with the topology of a four-dimensional sphere or a doughnut so that traveling far in one direction could bring you back from the opposite direction. The cosmic microwave background allows sensitive tests of such finite models, but has so far produced no support for them — flat infinite models fit the data fine and strong limits have been placed on both spatial curvature and multiply connected topologies. In addition, a spatially infinite universe is a generic prediction of the cosmological theory of inflation (Garriga & Vilenkin 2001b). The striking successes of inflation listed below therefore lend further support to the idea that space is after all simple and infinite just as we learned in school.

So, it seems that unless Missler knows something all other physicists don’t, he is being much too hasty and cherry picking possibilities to support what he wants to be true.

In my quest to understand the true nature of reality, the ongoing dispute between theism and atheism is a regular subject of interest. Perhaps most noteworthy at present is the ‘battle’ over intelligent design. Is it a science or is it religion in disguise? Some deride it as a waste of time and a joke, others think it something to be addressed, but mistaken, and still others insist that it provides compelling evidence in favor of theism. I am of the persuasion that intelligent design is scientific in nature and worthy of consideration. As to the correctness of the endeavor, I’m skeptical, but willing to give it a fair hearing. This is what I would like to do in a series of blogs aimed at both understanding and critiquing intelligent design at a fundamental level. Since my background is in mathematics, I will primarily focus on this aspect of it as well as its philosophical underpinnings. My focus will be primarily on the work of Bill Dembski, a mathematician and philosopher championing the fundamental notions of intelligent design. Input from other disciplines, however, is most welcome.

To get things started, it will be important to have a commonly understood vocabulary. Since design is the backbone of intelligent design, understanding this term is a logical launching point. So, the question is: What is design? In their paper, Wesley Elsberry and Jeffrey Shallit (see here) criticize Dembski, in part, on the grounds that he gives no positive notion of what design is. In his book, The Design Inference, Dembski gives a negative definition of design as the complement of regularity and chance. In No Free Lunch, he gives a more process-oriented account of design:

(1) A designer conceives a purpose.

(2) To accomplish that purpose, the designer forms a plan.

(3) To execute the plan, the designer specifies building materials and assembly instructions.

(4) Finally, the designer or some surrogate applies the assembly instructions to the building materials.

Also, although I have not read Dembski’s book Intelligent Design, I cannot find (with the help of the index) any place where he explicitly defines design. So, this is task number one; namely, to supply an adequate definition for design. Anyone familiar with this topic is encouraged to contribute. For my part, here is something of a first draft:

Definition – Design: A system that is arranged by an intensional agent.

Terence Tao is a brilliant mathematician whom I follow. He posts about a lot of very interesting mathematical topics. I found this neat post related to formals systems. The beginning of the article should hopefully be at least somewhat familiar based on what I have discussed, but it does get heavy pretty quickly. Nevertheless, check it out and enjoy!

A few post ago I was talking about formal systems. As an example I talked a little about Hofstadter’s example of the MIU system and promised to talk about decision procedures. I would hate to be a liar and so I do plan on returning to this matter. However, it seems appropriate to me to take a diversion into the philosophical foundations of Tegmark’s view before delving into the more mathematical aspects. For this reason, and in keeping with the announcement of my previous post, I am going to interact a bit with David Lewis’ work On the Plurality of Worlds.

So, what is Modal Realism? From what I gather, the name was actually coined by Lewis, though he expresses certain regrets for calling it this based on some ambiguity in the term ‘realism’ and what it has come to mean in academia. As one who is less familiar with the larger body of literature on realism, I find the name perfectly appropriate and satisfying.

The term ‘modal’ comes from modal logic which analyses the notions of necessity and possibility. G.E. Hughes and M.J. Cresswell summarize this discipline similarly:

Modal logic can be described briefly as the logic of necessity and possibility, of ‘must be’ and ‘may be’.

‘Realism’ as Lewis intends to use it deals with ontology. Put together, modal realism is

… the thesis that the world we are part of is but one of a plurality of worlds, and that we who inhabit this world are only a few out of all the inhabitants of all the worlds.

In other words, modal realism takes possible worlds semantics quite seriously as well as literally. Upon reading this description, one may be tempted to think of modal realism as a multi-verse theory and indeed it is (we’ll see that it corresponds to Tegmark’s Level IV multiverse), but not in the sense often portrayed in popular literature. The worlds of modal realism are not some distant universes located some vast, albeit finite, distance away. Nor are they located in some alternate dimension of this reality. As Lewis puts it,

They are isolated; there are no spatiotemporal relations at all between things that belong to different worlds. Nor does anything that happens at one world cause anything to happen at another.

One should liken this to the way in which the vector space is isolated from the finite field , to sneak in some mathematics.

Lewis goes on to say,

The difference between this and the other worlds is not a categorial difference. Nor does this world differ from the others in its manner of existing. I do not have the slightest idea what a difference in manner of existing is supposed to be. [emphasis mine]

Thank you!!! I expressed this very sentiment in A Philosophical Interlude. It always feels amazing when one’s own thoughts are legitimized by world renown experts. Okay, enough tooting my own horn. The idea, here, is that some things exist, say, on Earth, while other things exist elsewhere and this is a difference in location of existing things (not a difference in any mode of existence). Similarly, though somewhat more controversial, some things exist in the past, others now and still others in the future. This is a temporal difference (we will deal with the nature of time in another post). To extend this further, it seems reasonable that the same could be said for worlds. Some things exist in this world and other things exist in other worlds and this is still a difference between existing things as opposed to a difference in any mode of existing.

For those not familiar with the language of possible worlds, I should hasten to point out that a world need not be a synonym for a universe (though it might be). Rather, a world is a complete state of affairs, an entire reality. Thus, in our world, if there is a God who created the universe, then clearly our world is more than just our universe. Alvin Plantinga in his book The Nature of Necessity defines a possible world to be a maximal state of affairs and a maximal state of affairs is one such that for every state of affairs , includes or precludes . Note the similarity of this definition with that of completeness for a mathematical system:

A system is complete if, for every statement , we can find a proof of , or a proof of not-.

Here “proof” refers to a demonstration within the system in question using the axioms and the rules of inference. In other words, a “proof”, here, of a statement within a system “consists of a sequence of statements, each of which is either an axiom or a logical consequence of certain preceding statements in the list, such that the last statement in the list is .”

At this point, we needn’t get bogged down in technicalities. The basic idea is that modality is best understood by actually taking possible worlds semantics as more than just semantics. According to modal realism, all possible worlds are actual worlds, where actuality is taken to be indexical.

The task I have determined to undertake here is a formidable one. Despite this, I am excited about adding in some key works of David Lewis. From Amazon:

David Lewis (1941- 2001) was Professor of Philosophy at Princeton University. His publications include Convention (reissued by Blackwell 2002), Counterfactuals (reissued by Blackwell 2000), Parts of Classes (1991), and of numerous articles in metaphysics and other areas.

The books I plan on reading are On the Plurality of Worlds and Counterfactuals. Here is the description of former:

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

After putting forward the type of modal realism he favors, Lewis answers numerous objections that have been raised against it. These include an insistence that everything must be actual; paradoxes akin to those that confront naive set theory; arguments that modal realism leads to inductive skepticism, or to disregard for prudence and morality; and finally, sheer incredulity at a theory that disagrees so badly with common opinion. Lewis grants the weight of the last objection, but takes it to be outweighed by the benefits to systematic theory that acceptance of modal realism brings. He asks whether these same benefits might be gained more cheaply if we replace his many worlds by many merely ‘abstract’ representations; but concludes that all versions of this ‘ersatz modal realism’ are in serious trouble. In the final chapter, Lewis distinguishes various questions about trans-world identity, and argues that his ‘method of counterparts’ is preferable to alternative approaches.

Here is a description of the latter:

Counterfactuals is David Lewis’s forceful presentation of and sustained argument for a particular view about propositions which express contrary-to-fact conditionals, including his famous defense of realism about possible worlds. Since its original publication in 1973, it has become a classic of contemporary philosophy, and is essential reading for anyone interested in the logic and metaphysics of counterfactuals.

If it is not already obvious, the purpose of including these works is that they (especially the former) provide the philosophical groundwork underpinning Tegmark’s ideas. As I mentioned before, the MUH is a form of modal realism and could be described as a mathematized version of Lewis’s philosophy.

Since I am already addressing Tegmark’s ideas along with Hofstadter’s I hope to not become bogged down by adding in more, but the relevance of Lewis’s work in this matter seems justification enough to shoulder the burden. I hope everyone who reads this is as excited as I am to engage these ideas!